In systems, such as wireless communications systems, services are provided to users based on the allocation of shared finite resources that are limited. The allocation of these resources can encounter conflicting goals. For instance, favoring a certain class of users may increase the system's efficiency, but may result in the dissatisfaction of other classes of users. In contrast, providing equal services to all users may result in higher fairness but low efficiency. Using a trade-off policy to control the emphasis placed on various goals can result in wasteful allocation of resources, and less than optimal efficiency and fairness. For example, a benefit can be defined as the rates of data delivered to the users. The rates are controlled by appropriate allocation of radio resources at the transmitters. The transmitters may allocate their resources in such a way that maximizes the sum of the rates delivered to the users. This allocation favors users that are geographically closer to the transmitter at the expense of farther users. Although more efficient from the system's perspective, such allocation is unfair to users at less advantageous locations. A fairer allocation is one in which the minimum rate received by the users is maximized. However, this allocation can result in unacceptable system efficiency, e.g., a low sum rate. Hence, there is a need for a better mechanism to find an optimal trade-off policy that allocates resources with higher efficiency and at the same time higher fairness to the users.